The present invention relates to Coriolis mass flow rate meters that include oscillating flow conduits. The flow conduits used in these Coriolis mass flow rate meters are mounted so they can oscillate at resonance frequencies about at least two axes. One of the axes is associated with externally applied forces used to oscillate each flow conduit. The other axis is associated with deflections of each flow conduit caused by Coriolis forces arising from the combination of the driven oscillation and flow of fluids through the flow conduit. For the present invention the flow conduits are designed so as to have the ratio of both resonance frequencies remain constant even when the mass of the flow conduits change because the density of the fluid passing through the flow conduits changes.